# Uses toys in a day. The cost of

Uses of mathematics for all vendors
G.J.JULIA PRINCESS, Asst. Professor,
DEPARTMENT OF MATHEMATICS.
Mathematics is very useful and everyday maths is all around us. Mathematics is necessary for all the people in the world. Even if they are uneducated they know basic calculations like addition, subtraction, multiplication and division for their needs. Vendors and grocers use it for calculating the bills.
In everyday life, In home it is useful for making budgets, In EB office it is useful for calculating the current supply, In business it is useful in accounting like expenditure, salary for the staff and etc…,so maths is essential in day-to-day life for all who earns and expenses money.
Algebraic equations are in everyday to calculate the amount, number of items and etc..,
How Algebra is useful for finding the production of a company:
For example, A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On the particular day, the total cost of production was Rs.750.We would like to find out the number of toys produced on that day.
Solution:
Let the number of toys produced on that day be ‘x’
The cost of production (in rupees) of each toy that day = 55 – x
So. the total cost of production (in rupees) that day = x (55-x)
Therefore,
x (55 – x) = 750
55x – x2 =750
x2 – 55x + 750 = 0
Hence the value of x is x = 30 or 2
Similarly, Arithmetic Progression is the pattern in which succeeding terms are obtained by adding a fixed number to the preceding terms. And also we shall find the nth term and the sum of n consecutive terms, Now we have to see how it is applicable in our daily life.
An arithmetic Progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
Arithmetic Progression (A.P) is also used to find the production of a company:
For example,
A manufacturer of TV sets produced600 sets in the third year and 700 sets in the seventh year, find the production in the first, tenth year and the total production in first seven years.
Since the production increases uniformly by a fixed number of TV sets manufactured in 1,2,3……years will form an A.P.
We denote the No. of TV sets in the nth year by an. then a3=600 a7=700
Since, an=a+(n-1)d , a+2d=600 ;a+6d=700
Solving these two we get d=25 & a=550
(i)Production in the first year is 550
(ii) Production in the tenth year = a+(10-1)d =550+(9*25) =775
(iii)Total production is Rs.4375 , Since Sn= n/2(2a+(n-1)d).

Percentages are very useful in the marketing field:
In marketing, the sales Representatives should prepare “The stock and sales report” by giving – opening stock, Primary stock, Secondary stock and Closing stock details to their companies and also give the growth percentage(%).RDS wise stock and sales also prepared.
The percentages are used for finding discount %, Tax %, Profit %, Loss% and etc.., for all vendors. Profit%=profit/(cost price) *100
Loss %=Loss/(cost price) *100
For example,
A man buys a wrist watche for Rs.15200 and sells it at a loss of20%.what is the selling price of the watch?
C.P=Rs.15200 ; Loss=20% ; S.P=(100-Loss%)/100 × C.P.=Rs.12160.

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